In semiconductor manufacturing, devices, such as transistors, may be produced on a semiconductor wafer and interconnected to form integrated circuits (ICs) that perform numerous useful functions. The ICs may be packaged and sold. Forming the devices typically includes numerous steps of photolithography that provide patterns on the wafer surface.
Photolithography typically includes forming a photosensitive film on a wafer, exposing the film with a pattern by projecting radiation through a mask to chemically alter the film, and developing away exposed or unexposed portions of the film so a patterned film remains on the wafer.
Typically, masks may be designed using the characteristics of the photolithography equipment, including the optics and illumination source, and the desired pattern. Often, the photolithography equipment is designed to enhance resolution, such that small features may be patterned. Resolution, R, may be defined as the smallest obtainable half pitch and may given by:
      R    =          k      ⁢                          ⁢      1      ⁢              (                  λ          NA                )              ,where λ is the radiation wavelength, NA is the numerical aperture of the optics, and k1 is a constant based on the photolithography system (including the equipment, the photoresist, and the mask). NA relates to the angular aperture, α, of the lens (the angle between a line from the focal point to the center of the lens and a line from the focal point to the aperture) and is given by:
      NA    =          I      ⁢                          ⁢              sin        ⁡                  (                      a            2                    )                      ,where I is the refractive index of the medium the optics are in (typically air, such that I is 1.0).
Although a low k1 is desired to improve resolution, as k1 is pushed lower, it may become difficult to design masks. Therefore, mask designs may be restricted by design rules, based on the photolithography system, that hinder production of a desired pattern. In particular, photolithography tool resolutions of about k1 equal to 0.33 may provide severe design rule restrictions.
Further, after designing a mask, it may be determined that the mask is not manufacturable and the pattern may have to be abandoned and replaced. Such abandonment and replacement can increase the cost and time of producing the masks.